(dy)/(dx)=(1+y^2)e^x

Lösung

\frac{d y}{d x} = (1 + y^{2}) e^{x}

y = tan (e^{x} + c_{1})

Schritte zur Lösung

\frac{d y}{d x} = (1 + y^{2}) e^{x}

Solve separable ODE:

y = tan (e^{x} + c_{1})

y = tan (e^{x} + c_{1})

(- y^{2} + 2 y) d x + (x y - x) d y = 0

y^{^{'}} + 2 y = 11

(1 - x^{2})^{\frac{1}{2}} y^{^{'}} = (y^{2} - 2 y + 1) arcsin (x)

\frac{d y}{d x} = 8 x y

y^{^{'}} = y^{(\frac{1}{2})}